Subject: [mg44406] RE: [mg44358] Part 2 of a recent post on Plot and v 5

From: "David Park" <djmp at earthlink.net>

Date: Sat, 8 Nov 2003 04:50:49 -0500 (EST)

Sender: owner-wri-mathgroup at wolfram.com

Mariusz,
Selecting the "interesting" portion of a plot is not a new feature in
Mathematica. I don't think the algorithm is public and it has apparently
changed between Version 4 and 5. Even if you had the algorithm it probably
wouldn't help much in predicting the plot outcome in advance.
Would you prefer that PlotRange -> All be the default, instead of
PlotRange -> Automatic? Then what would you think of the following plot?
Plot[Tan[x], {x, -10, 10},
PlotRange -> All]
It might seem that it would be more reasonable to have Mathematica adjust
the y range and leave the x range untouched. But what about other plot types
such as ParametricPlot or ImplicitPlot? Mathematica cannot always tell which
axes you consider to be more fundamental.
The Mathematica plot types make great plots for many common cases with very
minimum coding. But this is deceptive. In many other cases one is just going
to have to add options and perhaps more complicated coding to get a
desirable plot. There is no way that a simple Plot command is going to be
able to make the correct choices for every case thrown its way. In any case,
the "correct" choice may very much depend upon the user's personal
preferences.
Good graphics is an art and in most cases you are going to have to work with
it a little. Whatever graphics program you use will have some conventions
that you will have to live with. There is a perfectly simple method to make
your plot come out the way you want. If your position is that you don't ever
want to add an option, then I think that is both unrealistic and unwise.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Mariusz Jankowski [mailto:mjankowski at usm.maine.edu]
To: mathgroup at smc.vnet.net
Dear colleagues, I recently posted a question about the apparent change to
Plot in version 5. I gather from the responses (thank you) that this new
feature seemed natural or even desirable. That surprised me, so let me
explain.
I used
Plot[UnitStep[x], {x, -1, 5}];
and found that Mathematica chose to display the function in the "more
interesting" range of -1<=x<=1.
My opinion is that an EXPLICITLY given range in any of the graphics commands
should not be overridden, under any circumstances. Is there anyone who
agrees with me? I would love to hear some of the opinions for and against,
especially the former, because I can't think of any.
Finally, if this indeed is a new feature, can anyone explain the algorithm
that is used to choose the "interesting" interval and is it used in any
other 2D graphic functions, and density or contour plots?
Thanks, Mariusz